Seminar: Multiscale Modeling of Heterogeneous Granular Systems Alberto M. Cuitiño Mechanical and Aerospace Engineering Rutgers University Piscataway, New Jersey [email protected] IHPC-IMS Program on Advances & Mathematical Issues in Large Scale.
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Seminar: Multiscale Modeling of Heterogeneous Granular Systems Alberto M. Cuitiño Mechanical and Aerospace Engineering Rutgers University Piscataway, New Jersey [email protected] IHPC-IMS Program on Advances & Mathematical Issues in Large Scale Simulation (Dec 2002 - Mar 2003 & Oct - Nov 2003) Institute of High Performance Computing Institute for Mathematical Sciences, NUS Collaborators • Gustavo Gioia • Shanfu Zheng Singapore 2003 cuitiño@rutgers Rutgers 1. 2. 3. 4. 5. 6. 7. 8. 9. Harvard University William and Mary Yale University Princeton University Columbia University University of Pennsylvania Brown University Rutgers University (1766) Dartmouth Rutgers University RU Singapore 2003 cuitiño@rutgers Rutgers Rutgers University Newark New Brunswick Camden NYC Philadelphia Singapore 2003 cuitiño@rutgers College Ave Livignston Busch Douglass Cook Rutgers, New Brunswick Singapore 2003 cuitiño@rutgers Hairston Leads Rutgers Past Navy 48-27 SEPTEMBER 27, 2003 Golf Stadiumand Engineering Science Rutgers, Busch Singapore 2003 cuitiño@rutgers Design and Dynamics Thermal Sciences Fluid Mechanics Solids, Materials and Structures Haym Benaroya Haim Baruh Zhixiong (James) Guo Doyle D. Knight William Bottega Hae Chang Gea Yogesh Jaluria Michael R. Muller Alberto Cuitiño Noshir A. Langrana Constantine E. Polymeropoulos Timothy Wei Mitch Denda Constantinos Mavroidis Kyung T. Rhee Abdelfattah M.G. Zebib Entrance Ellis Dill M. Madara Ogot Stephen D.Zabusky Tse Norman J. Andrew Norris DajunShan Zhang Jerry Rutgers, Engineering Assimina S. Bachi Pelegri Kook Pae Tobias Rossman George Weng Singapore 2003 Rutgers, Mechanical and Aerospace cuitiño@rutgers Current Research • • • • • • • • Granular Systems (G. Gioia and S. Zheng) Crystal Plasticity Multiscale Modeling Foam Mechanics Folding of Thin Films Microelectronics Digital Image Correlation Computational Material Design (Ferroelectric Polymers) Singapore 2003 Support from NSF, DOE, DARPA, FAA, NJCST, IFPRI, CAFT is gratefully acknowledged cuitiño@rutgers Damage due to Electromigration in Interconnect Lines Sequence of pictures showing void and hillock formation in an 8µm wide Al interconnect due to electromigration (current density 2x107 A/cm², temperature 230°C) Thomas Göbel (t.goebel@ifw-dresden .de), 18.04.02 Singapore 2003 cuitiño@rutgers E 0, s = 0 V Schimschak and Krug, 2000 T Schimschak and Krug, 2000 Singapore 2003 cuitiño@rutgers Grain Boundary Effects VOID MOTION @ GRAIN BOUNDARY Initial Defect Grain 1 Grain 2 VOID RELEASE From GRAIN BOUNDARY VOID TRAPPING by GRAIN BOUNDARY Atkinson and Cuitino ‘03 Singapore 2003 ecuitiño@rutgers Goal Load Understand and quantitatively predict the MACROSCOPIC behavior of powder systems under compressive loading based on MICROSCOPIC properties such as particle/granule behavior and spatial arrangement Need for MULTISCALE Study Singapore 2003 PARTICLES (discrete) POWDERS (continuum) cuitiño@rutgers Background Macroscopic Compaction Curve Compaction Force 1 3rd Stage .9 0 Relative Density .8 0 .7 0 1st Stage .6 0 2nd Stage .5 0 0th Stage .4-4 0 0 1 -3 0 1 -2 0 1 -1 0 1 e rc o nF tio c a p m o dC e liz a rm o N Singapore 2003 cuitiño@rutgers Stages Mixing Die Filling Large Deformation Singapore 2003 Rearrangement Localized Deformation cuitiño@rutgers Identifying Processes and Regimes Mixing Discharge Transport Die Filling Granulation Vibration Early Consolidation Consolidation Precompression Compact Formation Characteristics: Characteristics: Characteristics: Characteristics: Characteristics: • Large relative motion of particles • Large relative motion of particles • Limited relative motion of particles • No relative motion of particles • No relative motion of particles • Differential acceleration between particles • Differential acceleration between particles • Low particle acceleration •Low acceleration • Low acceleration • Same neighbors • Same neighbors • Large number of distinct neighbors • Large number of distinct neighbors •Quasi-static •Quasi-static • Low forces among particles • Low forces among particles • Sizable forces among particles • Large forces among particles • Long times, relatively slow process • Short times •Small particle deformation (elastic + plastic) • Large particle deformation • Transient • Same neighbors • Quasi-static • Low forces among particles • Small particle deformation (elastic) • Quasi steady state Singapore 2003 cuitiño@rutgers Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Mixing Discharge Transport Die Filling Granulation Vibration Precompression PD/DEM/MC PD/DEM/MC PD/DEM/MC Consolidation Compact Formation GCC GQC Ballistic Deposition Numerical tools appropriate for process Singapore 2003 OUR SCOPE cuitiño@rutgers Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Mixing Discharge Transport Die Filling Granulation Vibration Precompression PD/DEM/MC PD/DEM/MC PD/DEM/MC Consolidation Compact Formation GCC GQC Ballistic Deposition Numerical tools appropriate for process Singapore 2003 OUR SCOPE cuitiño@rutgers Die Filling Cohesion Open Configuration Numerical Experimental Singapore 2003 No Cohesion Dense Configuration Numerical Experimental cuitiño@rutgers Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Mixing Discharge Transport Die Filling Granulation Vibration Precompression PD/DEM/MC PD/DEM/MC PD/DEM/MC Consolidation Compact Formation GCC GQC Ballistic Deposition Numerical tools appropriate for process Singapore 2003 OUR SCOPE cuitiño@rutgers Rearrangement Process by which open structures collapse into dense configurations • Cohesive Powders are susceptible to rearrangement while • Non-Cohesive Powders are not X-Ray Tomography-Density Maps Al2O3 Granules. Diameter = 30 microns Lannutti, 1997 Punch Video Imaging Glass Beads, Diameter = 1.2 mm Gioia and Cuitino, 1999 Increasing Pressure Singapore 2003 Increasing Pressure cuitiño@rutgers A physical description Convexification implies coexistence of two phases Energy landscape exhibits a Spinoidal Structure (nonconvex) Total H H Singapore 2003 H cuitiño@rutgers A relaxation mechanism Particle Rearrangement Mechanism Snap-Through of Rings (Kuhn et al. 1991) Ring Structures in Cohesive Powders Numerical Experimental Singapore 2003 cuitiño@rutgers Relaxation process Numerical Experimental Singapore 2003 cuitiño@rutgers Experiments and Theory Experimental Theoretical Kong et al., 1999 Al2O3 Singapore 2003 cuitiño@rutgers 2D: simulation and experiment Singapore 2003 cuitiño@rutgers Rearrangement Front Experiment Singapore 2003 Simulation cuitiño@rutgers “Grains” Singapore 2003 cuitiño@rutgers 2D Simulations (Size Distribution) Singapore 2003 cuitiño@rutgers 3D Simulations Singapore 2003 cuitiño@rutgers Comparison with Experiment Mueth, Jaeger, Nagel 2000 Singapore 2003 Experiment Simulation cuitiño@rutgers Further Predictions Experiment Singapore 2003 Simulation cuitiño@rutgers Particle Rearrangement 3D • Homogeneous particle size; • r = 0.5 mm; r = 0.5mm • Particles = 120,991 Singapore 2003 cuitiño@rutgers Quantitative Predictions (a) = 0.627 0.65 •Rearrangement front; 0.6 u=7.5 u=5.0 u=2.5 =0.51 0.5 0.45 •Density increase; u=9.1 0.55 0 10 20 30 40 50 (b) 1 •Contact number increase; u=7.5 0.5 u=5.0 u=2.5 u=0.25 0 0 10 20 30 40 50 (c) 1 u=9.1 h / •Relative movement stops; v / u=9.1 0.5 u=2.5 u=5.0 u=7.5 u=0.25 0 0 (d) 10 6.5 20 30 40 Nc = 6.27 u=9.1 6 Nc 50 u=0.25 5.5 5 u=7.5 4.5 4 Singapore 2003 0 u=5.0 10 20 u=2.5 30 40 50 cuitiño@rutgers Heterogeneous System (Same Material) •Log-normal distribution; d = 2.16 ~ 9.10 mm; particles=13,134 Without rearrangement Singapore 2003 After rearrangement cuitiño@rutgers Multiphase Systems Singapore 2003 cuitiño@rutgers Identifying Numerical Tools (which can use direct input from finer scale) Early Consolidation Mixing Discharge Transport Die Filling Granulation Vibration Precompression PD/DEM/MC PD/DEM/MC PD/DEM/MC Consolidation Compact Formation GCC GQC Ballistic Deposition Numerical tools appropriate for process Singapore 2003 OUR SCOPE cuitiño@rutgers Granular Quasi-Continuum FEM Mesh Set of Particles Constrain kinematics of the particles by overimposing a displacement field described by a set of the displacements in a set of points (nodes) and a corresponding set of interpolation functions (a FEM mesh) Singapore 2003 Combined System A quasi-continuum approach cuitiño@rutgers Governing Equations P PVW Euler Equation P 8m 2P 8n 2Vm 1 mn î w 2 + P m f áî u m = 0 8m 2P 1dî wmn m + f = 0 mn 8n 2Vm 2 dr P Local Equilibrium Singapore 2003 cuitiño@rutgers Force Fields • Plastic deformation follows similarity solution; Contacts on each particle are independent. • Volume change after inter-particle voids are filled in. -1200 volume changed r2 d -800 = r1 + r2 - d -600 Hertzian contact -400 -200 Similarity solution 0 Singapore 2003 r1 -1000 Force • Elastic contact follows Hertz contact law; 0 0.1 0.2 Indentation () 0.3 cuitiño@rutgers Role of FF parameters - sy 1 • Effect of yielding stress is significant; • Solidification force differ significantly but the solidification density relative unchange. sy = 0.1 0.9 Density (g/cm3) • Lower sy yield higher deformation under the same pressure and thus higher density; sy = 0.01 sy = 1 (in MPa) 0.8 HDPE 100 E = 1 GPa n=3 = 0.3 0 = 1.1 g/cm3 0.7 0.6 0.5 0 Singapore 2003 2 4 6 Force (kN) 8 10 cuitiño@rutgers Role of FF parameters: hardening 1 • Soft material (n) is easy to be solidified. 0.9 Density (g/cm3) • Effect of hardening parameter n is significant; n= n = 10 0.8 HDPE 100 E = 1 GPa n=3 sy = 1 MPa = 0.3 0 = 1.1 g/cm3 0.7 0.6 0.5 0 Singapore 2003 2 4 6 Force (kN) 8 10 cuitiño@rutgers Role of FF parameters: Poisson’s ratio 1 = 0.2 Density (g/cm3) 0.9 = 0.3 0.8 HDPE 100 E = 1 GPa sy = 1 MPa n=3 0 = 1.1 g/cm3 0.7 0.6 0.5 0 Singapore 2003 2 4 6 Force (kN) 8 10 cuitiño@rutgers Case of Study: Multiphase System Singapore 2003 cuitiño@rutgers Spatial Distribution Phase I Phase I Phase I Variant 1 Variant 2 Variant 3 Singapore 2003 cuitiño@rutgers Spatial Distribution Phase II Variant 1-4 Singapore 2003 cuitiño@rutgers Spatial Distribution Phase III Needs an uniform distribution Singapore 2003 cuitiño@rutgers Multiphase System Rearrangement Full mixed + Cohesion force Singapore 2003 cuitiño@rutgers Multiphase System Post-Rearrangement Input for GQC Singapore 2003 cuitiño@rutgers Calibration of FF Detergent Granule 1 1.5 1.4 Density (g/cc) 1.3 1.2 1.1 Sample: mass = 0.75 g size = 1212 6.6 (red) 1212 5.8 (blue) density = 0.789 g/cc (red) 0.898 g/cc (blue) Particles: size = 0.216 ~ 0.91 mm number = 13,134 1 0.9 0.8 0.7 0.6 0.5 0 Singapore 2003 1 2 3 4 stress (MPa) 5 6 7 cuitiño@rutgers Multiphase System Comparison with Experiment MACROSCOPIC Behavior • At early stage of experiment the deformation is the mainly from the particle rearrangement. 1.2 density (g/cc) • Density diversity at initial state is mainly due to the irregular shape of real particles; 1.3 1.1 1 0.9 Sample : mass = 0.075 (g) 3 size = 55 3.3 (mm ) density = 0.91 (g/cc) particle size = 0.1~0.5 (mm) particles = 7,986 0.8 0.7 0.6 Singapore 2003 0 0.5 1 1.5 2 stress (MPa) 2.5 3 cuitiño@rutgers Multiphase System: density evolution Full Field Predictions Z dens: 0.68 0.78 0.87 0.97 1.06 1.16 1.25 1.35 X Y 6 Z 4 2 0 0 0 2 Movie Here 2 4 Y 4 6 6 8 8 10 Singapore 2003 X 10 cuitiño@rutgers Multiphase System: pressure evolution Z X Y 6 Z 4 2 0 0 Movie Here 0 2 2 4 Y 4 6 6 8 8 10 Singapore 2003 X 10 cuitiño@rutgers Granular Quasi-Continuum GOOD • Allows for explicit account of the particle level response on the effective behavior of the powder • Provides estimates of global fields such as stress, strain density • Is numerically efficient, can also be improved by using stochastic integration • Provides variable spatial resolution Singapore 2003 BAD • Is not well posed to handle large nonaffine motion of particles • Particle deformation is only considered in an approximate manner (as in PD/DEM) cuitiño@rutgers Towards Computationally Aided Material Design ACCEPTABLE RANGE OF NANOCOMPOSITE PARAMETERS ACCEPATLE MAXIMUM PORE SIZE FORCE PARAMETERS NANO COMPOSITE PARAMETERS PORE SIZE ACCEPTABLE RANGE OF FORCE PARAMTERS TO NANO SCALE Singapore 2003 MICRO SCALE cuitiño@rutgers Summary and conclusions • Powder compaction is a complex process where many dissimilar entities (particles) consolidate by various concurrent mechanisms. • In the low pressure regime, rearrangement and localized particle deformation dominates the mechanical response. • In this initial regime, compaction proceeds in a discontinuous fashion by an advancing front. • The physics of the rearrangement can be traced to a spinoidal structure in the energy density of the system. • This process can be theoretically described using the framework of non-convex analysis. • The effect of particle deformability and die wall roughness are incorporated into the analysis in a clear and physical manner. • Numerical simulations verify the theoretical model • Experimental studies validate the model and simulations • 3D simulations show a similar behavior that 2D ones, indicating the same physics operates in 2D and 3D cases. Singapore 2003 cuitiño@rutgers